Homogenization of “Viscous” Hamilton–Jacobi Equations in Stationary Ergodic Media

By Pierre-Louis Lions, Panagiotis E. Souganidis. 2005

143 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/bcd632fada4e15a7b257324601223f4f33333f94

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications (2005, unknown): “In a subsequent work [27], the showed that in this case, in general, there are no correctors, i.”
Spreading speeds for one-dimensional monostable reaction-diffusion equations (2016, background): “The existence of classical eigenfunctions (called “exact correctors” in the homogenization literature) is an open problem in the general framework of nonlinear Hamilton-Jacobi equation (see [21]).”
Stochastic Homogenization of Level-Set Convex Hamilton–Jacobi Equations (2012, result): “As mentioned above, results for stochastic homogenization of first-order Hamilton-Jacobi equations were first obtained by Souganidis [25] and Rezakhanlou and Tarver [23] and, for viscous HamiltonJacobi equations, by Lions and Souganidis [21] and Kosygina, Rezakhanlou, and Varadhan [15].”
Stochastic Homogenization of Nonconvex Hamilton‐Jacobi Equations: A Counterexample (2015, background): “mentioned in the literature (see, for instance, [2, 7, 8, 14, 18, 19]).”
Stochastic homogenization of Hamilton‐Jacobi‐Bellman equations (2006, methodology): “In the special case of H(p, ω) = a(ω)‖p‖α with α > 1, in addition to uniform upper and lower bounds on a, we would need uniform continuity of a(τyω), whereas [13] would assume a uniform bound on the gradient in y of a(τyω).”
Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations (2012, methodology): “[32] P. E. Souganidis.”
50 years of first passage percolation (2015, methodology): “The advantage of such a perspective is to allow us to use the work of Lions-Souganidis [130,131] on certain homogenization problems in R to give a different characterization of the time constant.”
Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments (2011, methodology): “See for instance Carmona and Lacroix [5] as well as Section 8 of [23].”
Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media (2010, background): “In [ 21 ]t hey also established the stochastic homogenization of viscous Hamilton-Jacobi equations.”
Asymptotic and numerical homogenization (2008, methodology): “The proof of the theorem in Lions and Souganidis (2005a) is based strongly on the (stochastic) control interpretation of (5.6), which is available due to the assumptions that H is convex and A independent of Du, and the use of the (sub-additive) ergodic theorem.”
Stochastic homogenization of Hamilton-Jacobi equations in stationary ergodic spatio-temporal media (2009, methodology): “Moreover, counter examples to the solvability of the corrector problem with a strictly sublinear w were given in [21] and [22].”